ORVINUSOptions & Derivatives Pricing
The textbook gives you Black-Scholes. Markets give you smiles, skews, and surfaces — we build the models that price what's actually traded.
Options and derivatives pricing is the quantitative machinery for valuing contracts whose worth derives from other assets: options, futures, and structured positions. It spans closed-form models like Black-Scholes-Merton, lattice and Monte Carlo methods for path-dependent payoffs, Greeks computation for hedging, and the volatility modeling that feeds all of it.
Production pricing is an engineering problem as much as a mathematical one: models must ingest live market data, calibrate to current prices, compute across full option chains fast enough to trade on, and degrade gracefully when quotes go stale or markets gap. That is the system we build — validated numerics inside reliable software.
Pricing and volatility models rarely stand alone: they feed signals, size positions, and drive risk analytics across the rest of the quant stack. Everything is delivered as documented code you own — with model assumptions written down, because a pricing model whose limits you don't know is a risk model you don't have.
Options and derivatives pricing models value options, futures, and structured contracts using methods such as Black-Scholes-Merton, lattice models, and Monte Carlo simulation, supported by volatility and statistical modeling. ORVINUS builds production pricing engines with Greeks computation, implied-volatility surfaces, GARCH forecasting, and calibration to live market data.
Options & Derivatives Pricing Models
We implement the pricing stack appropriate to your instruments: Black-Scholes-Merton for European options, binomial and trinomial lattices where early exercise matters, and Monte Carlo engines for path-dependent and multi-asset payoffs — each validated against known analytical solutions and observed market prices before it prices anything real. Greeks (delta, gamma, vega, theta, rho) are computed alongside, analytically where closed forms exist and numerically where they don't, because a price without its hedging sensitivities is half a model.
Engineering makes the mathematics usable: calibration routines fitting model parameters to live quotes with fit diagnostics, full option-chain pricing at speeds that respect trading decisions, implied-volatility solvers hardened against stale and crossed quotes, and caching so repeated computation doesn't burn latency. The models run behind clean APIs that your strategies, risk systems, and dashboards consume as production services — versioned, monitored, and rebuilt against market data on every calibration cycle.
Volatility & Statistical Modeling
Volatility is the input that decides whether a pricing model tells the truth. We build volatility modeling matched to the use: historical and realized-volatility estimation across horizons, GARCH-family models for forecasting, implied-volatility surface construction with arbitrage-consistency checks, and term-structure analysis across expiries. Surfaces update continuously from live option-chain data with filtering for bad quotes, so the volatility feeding your prices reflects the market as it is, not as it was an hour ago.
Statistical modeling extends beyond volatility into the analysis a quant operation runs on: distribution analysis that respects fat tails instead of assuming them away, correlation and cointegration analysis for pairs and portfolio construction, and regime detection that feeds strategy and sizing logic. Every model ships with its assumptions and failure modes documented and its forecasts validated out-of-sample — statistical machinery you can interrogate, not a black box you're asked to trust.
Built With
The technologies we reach for on this work — and why we use each one.
See what we use every tool for in the full technology stack.
What You Get
Pricing engine
Validated pricing models with full Greeks, calibration, and implied-volatility solvers behind clean, documented APIs.
Volatility models
Realized, forecast, and implied-volatility modeling — including surface construction with consistency checks.
Validation dossier
Model outputs verified against reference solutions and market prices, with assumptions and limits documented.
Integration layer
Pricing and volatility feeds wired into your strategy, risk, and analytics systems as production services.
Other Algorithmic Trading Specializations
Trading Strategy Development
Trading ideas engineered into precise, testable strategy logic — indicator systems, multi-timeframe rules, and pattern recognition.
Explore Strategy DevelopmentBacktesting & Risk Modeling
Historical validation you can trust — backtesting engines with honest cost modeling, risk frameworks, and portfolio optimization.
Explore Backtesting & RiskAutomated Execution Systems
From signal to filled order without a human in the loop — low-latency execution with failsafes, monitoring, and 24/7 operation.
Explore Automated ExecutionTrading Analytics & Reporting
Performance dashboards, P&L tracking, and real-time charting — the instrumentation a serious trading operation runs on.
Explore Trading AnalyticsWhere This Work Lands
Common Questions
Which pricing models do you implement?
The model follows the instrument: Black-Scholes-Merton for European options, binomial and trinomial lattices for American-style early exercise, and Monte Carlo for path-dependent or multi-asset payoffs. Every implementation is validated against known analytical solutions and observed market prices before it prices a live position — model choice is justified, not defaulted.
Can you build an implied-volatility surface from live data?
Yes. We construct surfaces from live option-chain quotes with filtering for stale and crossed prices, interpolation across strikes and expiries, and arbitrage-consistency checks — so the surface is usable for pricing and risk, not just plotting. Surfaces update continuously and are served through the same APIs as the pricing engine.
Do we need machine learning for pricing?
Usually not for pricing itself — classical models are fast, interpretable, and well understood. ML earns its place around them: learned volatility dynamics, regime detection, or fast approximations of expensive Monte Carlo pricing. We default to the classical model and add learning only when validation shows it improves the numbers you trade on.
How do you validate the models?
Layered checks: numerical verification against closed-form solutions, convergence testing for lattice and Monte Carlo engines, calibration-fit diagnostics against market prices, and out-of-sample testing for any forecasting component. Assumptions and known failure modes are documented with the delivery — the model's limits are part of the model.
Ready for Derivatives Pricing?
Free discovery call — we scope the work, name the trade-offs, and respond within 24 hours.